EP1894067B1 - Device for automatically adjusting the servo-controller of a mechanical motion simulator and simulator with such a device - Google Patents

Abstract

A tuning method for a motion simulator embarking a payload. The simulator includes a mechanical device, a mobile plate of which is capable of carrying a payload, and a control unit including a controller capable of position feedback controlling said plate. The method enables an automatic tuning of the controller in order to feedback control the system embarking a given payload.

Description

The subject of the invention is that of the servocontrol of the movement of a motion simulator.

A motion simulator is an assembly comprising a mechanical device and electronic and software units for controlling the mechanical device. The latter comprises a movable plate for receiving a load. The plate is able to be moved in rotation around one or more geometric axes and / or in translation along one or more geometric axes. In a Cartesian frame, for example terrestrial, the position of the solid that constitutes the plateau is given by the position of its center of gravity and the orientation of an axis perpendicular to the plane of the plateau.

A motion simulator can be an onboard positioner for positioning a given payload.

A motion simulator can also be a test bench for testing a load, such as an inertial system to be tested, during a sequence of controlled movements. The plate is then set in motion according to a predetermined sequence comprising a temporal succession of setpoint positions. At each instant, the kinematic parameters of the plateau deriving from setpoint in position can be compared to the kinematic parameters measured by the inertial system to be tested.

In order for the plate to follow precisely the position instructions, it is essential to use a servo loop in position of the plate.

On the figure 1 , there is shown a general diagram of a control loop of a motion simulator along an axis of rotation. The mechanical part of this servo loop comprises: the plate and its load mounted on a mechanical axis, the mechanical system 3 thus formed having a moment of inertia J with respect to its axis of rotation; the engine 2; the power amplifier 1; and, a position sensor 4. The power amplifier 1, in response to the control signal U, outputting a current I whose amplitude and step control the movement of the motor 2. The motor 2 generates a torque ┌ for rotating the mechanical system 3. The sensor 4 measuring, at each instant, the effective position y of the plate 3 and emits, at the output, a measurement signal giving a measurement Y of the position of the plate 3.

In general, the servo-control of a rotating machine consists in creating a feedback from the Y-measure of a magnitude y such as position, speed, etc. The purpose of this feedback is to allow effective monitoring of the desired quantity r. A correction or correction block 5 is generically defined as a component capable of transmitting a control signal U as a function of the setpoint r and of the measurement Y so that, for a given value of the setpoint r, the measured value Y converges to this value of the setpoint.

où les coefficients K_P, K_I et K_D sont ajustés de sorte que l'écart e tende le plus rapidement possible vers zéro lors d'un changement de la valeur de la consigne r.According to the prior art, the most frequently used servo corrector is of the PID type (proportional, integral, derivative) whose principle is described on the figure 2 . In this figure, in step 100, the measurement Y is first subtracted from the setpoint r. At the output of step 100, a gap e is obtained. The difference e is multiplied by a constant K _P in step 101, and the result obtained is fed into the input of an adder 110. At the same time, in step 102, the difference e is multiplied by a constant K _I then the result obtained is integrated with respect to the time in step 103. At the output of step 103, the result is applied to the input of the adder 110. At the same time, in step 104, the difference e is multiplied by the constant K _D , then derived with respect to time during step 105. The result of step 105 is emitted towards the input of the summator 110. Finally, the summator 110 is the sum of the different quantities that arrive at it to output the control signal U which is therefore of the form: $$\mathrm{U}\mathrm{=}{\mathrm{K}}_{\mathrm{P}}\mathrm{e}\mathrm{+}\mathrm{\lceil }{\mathrm{K}}_{\mathrm{I}}\mathrm{edt}\mathrm{+}\mathrm{d}\left({\mathrm{K}}_{\mathrm{D}}\mathrm{e}\right)\mathrm{/}\mathrm{dt}\mathrm{,}$$

where the coefficients K _P , K _I and K _D are adjusted so that the distance e tends as fast as possible to zero when a change in the value of the setpoint r.

• La robustesse : il s'agit de l'insensibilité du correcteur aux incertitudes de la modélisation physique de la machine à commander. Dans le cas spécifique d'un simulateur de mouvements, il faut que le correcteur soit robuste par rapport à la variation du moment d'inertie du système mécanique 3 lors du changement de la charge. En effet, un simulateur de mouvements servant à tester différentes charges, le moment d'inertie J du système mécanique est inévitablement modifié lors du changement de la charge. On dira qu'un correcteur est robuste lorsqu'il garantit la stabilité de la boucle d'asservissement fermée en cas de variation d'un ou de plusieurs paramètres physiques de la machine à réguler. Dans le cas d'un simulateur de mouvements ce paramètre est le moment d'inertie. Pour mémoire, la stabilité est l'aptitude du système asservi à se comporter de telle sorte que l'écart e tende vers une valeur finie lorsque la consigne r est modifiée. Mais, la convergence de la variable e peut se faire au bout d'un temps très élevé. C'est pourquoi il est également nécessaire d'introduire la notion de performance pour caractériser un asservissement.
• La performance : il s'agit de la dynamique de suivi de la consigne r et de la dynamique de rejet des perturbations pouvant affecter la machine. Dans le cas d'un simulateur de mouvements, les perturbations pouvant affecter le système sont, par exemple, constituées par un couple de freinage dû à des frottements non pris en compte.

Two main notions make it possible to characterize the servocontrol of a rotating machine:

• Robustness: this is the insensitivity of the corrector to the uncertainties of the physical modeling of the machine to be controlled. In the specific case of a motion simulator, the corrector must be robust with respect to the variation of the moment of inertia of the mechanical system 3 during the change of the load. Indeed, a motion simulator used to test different loads, the moment of inertia J of the mechanical system is inevitably changed during the change of the load. It will be said that a corrector is robust when it guarantees the stability of the closed servo loop in case of variation of one or more physical parameters of the machine to be regulated. In the case of a motion simulator this parameter is the moment of inertia. For the record, stability is the ability of the slave system to behave such that the gap e tends to a finite value when the setpoint r is changed. But, the convergence of the variable e can be done after a very long time. This is why it is also necessary to introduce the notion of performance to characterize an enslavement.
• Performance: this is the dynamics of monitoring the setpoint r and the dynamics of rejection of disturbances that can affect the machine. In the case of a motion simulator, the disturbances that may affect the system are, for example, constituted by a braking torque due to friction not taken into account.

From a theoretical point of view, it is shown that the objectives of performance and robustness are antagonistic. If one wishes high performance, that is to say that the system rejects disturbances very quickly, it is detrimental to the robustness.

For the motion simulators, the search for a maximum bandwidth leads to privileging the performance of the system compared to its robustness. In general, the robustness is relatively low which requires to adapt the corrector for each load.

Thus, the parameters of the corrector used, for example the gains K _P , K _I and K _D of the corrector of the type PID represented on the figure 2 , must be adjusted each time the load is changed.

According to the prior art, in the field of motion simulators, the adjustment of the corrector is done "manually" by the intervention of a technician in charge of the motion simulator each time the load of the simulator is modified. This setting is expensive in time and is empirical. Indeed, it requires many tests of the trial-and-error type to find the value of the adapted gains because the parameters of adjustment of the PID are dependent on each other. In addition, it is difficult to guarantee that the setting obtained corresponds to the optimum setting of the system. If the servo loop operates with a wrongly set corrector, the risk that the closed loop is not stable is not zero.

Procedures for automatically adjusting a corrector are known in other technical fields than that of motion simulators.

One technique consists in realizing an automatic real-time adjustment of the corrector parameters intended to slave a rotating machine during the use of the latter. This technique, known under the name of self-adaptive control ("self control"), is not transposable to the case of motion simulators because it is of great complexity especially since it is about respecting the constraint of 'real time' adjustment of the corrector. Moreover, there can be no precise knowledge of the movement since the parameters of the corrector are modified at every moment. This is especially true at the beginning of a sequence of movements, when the load has just been changed and the implementation of the adjustment procedure constantly changes the gains.

• Excitation du système avec un stimulus (changement du courant appliqué sur le moteur) ;
• Acquisition de la réponse de ce système à l'excitation appliquée ;
• Utilisation des données obtenues pour constituer un modèle mathématique du système (sous forme de fonction de transfert ou de modèle d'état) ; et,
• Utilisation du modèle obtenu pour synthétiser le correcteur.

Another technique used in the field of rotating machines is to perform an initial test step during which the corrector is set. The automatic adjustment of a corrector is done by respecting the following process:

• Excitation of the system with a stimulus (change of current applied to the motor);
• Acquisition of the response of this system to the applied excitation;
• Using the data obtained to form a mathematical model of the system (as a transfer function or as a state model); and,
• Using the model obtained to synthesize the corrector.

But, most of the time the excitation is done in open loop, that is to say without feedback. The user therefore does not know, a priori, what will be the acceleration, the speed or the displacement (excursion in position of the axis) of the movement.

In the case of a motion simulator, such a test is not possible in particular because, during the excitation stage of the system, constraints such as the maximum values of the acceleration, speed and the position must not be exceeded as this may damage the unit. It is therefore essential that this test be done in a controlled manner, that is to say with feedback to avoid the violation of constraints.

Jouve et al. IEEE 1991 Autotuning of axis control systems for robots and machine tools ] have proposed a method for performing an initial closed-loop test step in the case of a rotating machine which is a machine tool equipped with a speed sensor. It is therefore a servo loop speed.

This solution is not applicable to the case of motion simulators that are equipped with position sensors, extremely accurate, and rarely speed sensors, either expensive, noisy and inaccurate.

The use of a speed control loop, using a speed sensor, would not meet the constraints on the position of the movement during the test stage. In fact, the position would then be known only at an integration constant. This uncertainty about the value of the constant implies that we do not know where the movement will start and / or finish, which can lead to the crossing of stops and damage the motion simulator.

In addition, the article by Jouve et al. discloses a method that is actually specific to machine tools. Indeed, these last operate at high speeds, more than 5000 rpm, which are to be compared to the maximum speeds of about 500 rpm, operation of motion simulators. However, the methodology described can not be used at low speed, ie below a speed threshold, without the identification step being biased by nonlinear phenomena.

Finally, the article by Jouve et al. implicitly discloses the use of a low gain PI corrector for the initial test step. But in the case of a motion simulator, too small gains of a PID corrector (the PI is not adapted to a position loop) may result in an unstable closed loop.

Li et al. [Modeling, simulation and control of a hydraulic Stewart platform, IEEE 1997 , XP010235479] have proposed a method of controlling a Stewart platform for use as a motion simulator. The dynamic equations of the platform are derived from the virtual work principle, a robust and powerful controller is proposed but the on-line identification of the parameters of such a robust controller is not envisaged.

There is therefore a need for a method of automatically adjusting a position control loop for the case of a motion simulator. There is also a need for this automatic adjustment process to quickly achieve the desired performance / robustness compromise based on a given load.

For this purpose, the subject of the invention is an adjustment method implemented in a motion simulator capable of carrying a load, the simulator comprising a mechanical device and a control unit, the mechanical device comprising drive means for setting in motion a tray capable of carrying the load; a current amplifier adapted to actuate the drive means in response to a control signal; a sensor capable of measuring a position and the control unit comprising a corrector adapted to transmit the control signal as a function of a reference signal and the measured quantity.

• une étape initiale de synthèse d'un correcteur robuste, la synthèse étant fondée sur une première modélisation physique du dispositif mécanique comportant au moins un paramètre d'inertie, le correcteur robuste obtenu permettant l'asservissement du dispositif mécanique sur une plage de valeur du paramètre d'inertie s'étendant entre un paramètre d'inertie minimum et un paramètre d'inertie maximum ; et, après avoir positionné la charge donnée sur le plateau,
• une étape de test au cours de laquelle le dispositif mécanique, asservi au moyen du correcteur robuste déterminé lors de l'étape initiale, est actionné selon un profil de consigne de position prédéfini respectant des contraintes sur l'accélération, la vitesse et la position du mouvement, le signal de commande et la position mesurée étant mémorisés à chaque instant en tant que données de l'étape de test ;
• une étape d'identification qui, à partir des données de l'étape de test, permet de déterminer la valeur d'une pluralité de paramètres physiques d'une deuxième modélisation du dispositif mécanique embarquant la charge donnée, la pluralité de paramètres physiques comportant au moins le paramètre d'inertie ; et,
• une étape finale de synthèse d'un correcteur optimal adapté à la charge donnée, dans laquelle le paramètre d'inertie prend la valeur du paramètre d'inertie déterminé lors de l'étape d'identification.

The method according to the invention is characterized in that it makes it possible to automatically adjust the corrector to control the position of the movement of the mechanical device carrying a given load, the method comprising:

• an initial step of synthesis of a robust corrector, the synthesis being based on a first physical modeling of the mechanical device comprising at least one inertial parameter, the robust corrector obtained allowing the device to be servocontrolled mechanical over a range of value of the inertia parameter extending between a minimum inertia parameter and a maximum inertia parameter; and, after positioning the load given on the board,
• a test step during which the mechanical device, controlled by means of the robust corrector determined during the initial step, is actuated according to a predefined position reference profile respecting constraints on the acceleration, the speed and the position of the movement, the control signal and the measured position being stored at each moment as data of the test step;
• an identification step which, from the data of the test step, makes it possible to determine the value of a plurality of physical parameters of a second modeling of the mechanical device embodying the given load, the plurality of physical parameters comprising at least one minus the inertia parameter; and,
• a final step of synthesis of an optimal corrector adapted to the given load, in which the inertia parameter takes the value of the inertia parameter determined during the identification step.

Preferably, the mechanical device is able to put the board carrying a load at least in translation along an axis, the inertia parameter then being a mass of inertia.

Preferably, the mechanical device is able to put the board carrying a load at least in rotation about an axis, the inertia parameter then being a moment of inertia.

Preferably, during the initial step, the corrector is in a closed servo loop on a digital simulation of the mechanical device carrying a load having a nominal inertia parameter in the range.

Preferably, all the test, identification and final stages are performed again at least at each load change.

Preferably, the first modeling is a linear modeling of the dynamic behavior of the mechanical device.

Preferably, the robust and optimal correctors are synthesized with a LQG-H2 type methodology (optimization of the corrector according to a quadratic criterion) comprise a Kalman filter based on the first model, the Kalman filter taking, as input, the control signal, the measured quantity and the setpoint to generate, at the output, an estimated state of the mechanical device, estimated state being applied as control signal after being multiplied by a vector called state feedback vector.

Preferably, the Kalman filter makes it possible to estimate the disturbances affecting the mechanical device by modeling them by a signal coming to add to the control signal at the input of the mechanical device to be enslaved.

Preferably, the synthesis of robust and optimal correctors is made using a methodology called standard state control.

Preferably, the robust or optimal correctors comprise four high-level scalar control parameters.

Preferably, the initial step comprises first, by varying a first scalar parameter among the scalar parameters, the search for a corrector having a module margin greater than a threshold module margin for all the moment values of inertia of the range of moment of inertia, then, by varying another scalar parameter, said second parameter, among the scalar parameters, the search for a corrector having a delay margin greater than a threshold delay margin for all moment of inertia values of the moment of inertia range.

Preferably, the value of the moment of inertia having been identified, the final step comprises first, by varying the second parameter, the search for a corrector having a delay margin greater than the threshold delay margin, then , by still varying another scalar parameter, said third parameter, among the four scalar parameters, the search for an optimal corrector having a module margin greater than the threshold module margin.

Preferably, during the identification step, the second modeling is a linear modeling of the behavior of the device.

Preferably, during the identification step, the second modeling explicitly takes into account forces leading to a non-linear behavior of the device.

Preferably, the method comprises, at the end of the testing step, a preprocessing step to reject the data for which the corresponding value of the speed of the plate is lower than a threshold speed.

In order to perform a closed-loop position excitation test, it is necessary to design before this test a control law or corrector to ensure the stability of the motion simulator regardless of the inertia of the load placed on the machine plateau, the stability being characterized by a finite response of the system to a variation of the setpoint (absence of oscillations or divergence of the position of the axis with respect to the setpoint).

The fact of using a position control operating with a position sensor makes it possible to respect certain constraints of excursion of the plateau and not to risk the deterioration of the motion simulator. From this point of view, the invention has the advantage of being safe.

In addition, the invention presented here uses a modeling of the axis to be enslaved. Now some disturbing forces acting on the axis, depend explicitly on the position (unbalance), which requires the absolute knowledge of this position to develop the model of the axis.

The structure of the corrector used according to the invention as well as the methodology for synthesizing it depend on the particular application in the case of motion simulators.

In addition, from the moment when a position control is used, the synthesis of the robust corrector used is more complex. For example, the synthesis of a low gain PI corrector, such as that implicitly described in the article by Jouve et al., Is not sufficient. Advantageously, the robust corrector type LQG-H2 is synthesized by a methodology called standard state control.

Finally, the method according to the invention is particularly simple to use. It has the advantage of being able to be implemented by the end user of the motion simulator, which does not necessarily have to be a specialist in controlling the servo loop. The end user simply needs to specify for example the delay and module margins to be reached and to start the automatic procedure for summarizing the optimal corrector.

The invention also relates to a motion simulator capable of loading a load, the motion simulator comprising a mechanical device and a control unit, the simulator comprising a movable plate capable of carrying the load; drive means adapted to move the tray in at least one axis; a current amplifier adapted to actuate the drive means in response to a control signal; a sensor adapted to measure a position of the plate; the control unit comprising a corrector adapted to transmit the control signal as a function of a setpoint signal and the measured position, characterized in that the control unit is configured to implement one of the control methods. setting above to obtain an optimal corrector given a load.

In a first embodiment, the motion simulator is an onboard positioner, the given load being a payload.

In a second embodiment, the motion simulator is a test bench, the load given being a load to be tested.

• La figure 1 est un schéma général d'une boucle d'asservissement d'un simulateur de mouvements ;
• La figure 2 est un schéma général d'un correcteur selon l'art antérieur du type PID pour une mise en oeuvre dans la boucle d'asservissement de la figure 1 ;
• La figure 3 est un schéma-bloc représentant le principe de la méthodologie dite de contrôle d'état standard au moyen d'un correcteur intégrant un filtre de Kalman et un retour sur un état estimé du dispositif mécanique, utilisé dans le procédé selon l'invention ;
• La figure 4 est un diagramme représentant, sous la forme d'un algorithme, l'étape initiale du procédé selon l'invention permettant d'obtenir un correcteur robuste vis-à-vis des paramètres du système à contrôler ;
• La figure 5 représente de manière schématique la boucle d'asservissement dans l'étape de test du procédé selon l'invention ;
• La figure 6 est un graphe représentant la position correspondant à la consigne appliquée en entrée du correcteur de la figure 5 au cours de l'étape de test ;
• La figure 7 est un diagramme représentant, sous la forme d'un algorithme, l'étape du procédé selon l'invention permettant la détermination d'un correcteur optimal adapté à la charge.

The invention will be better understood and other objects, details, characteristics and advantages thereof will appear more clearly in the description of a particular embodiment of the invention given solely for illustrative and non-limiting purposes. in the accompanying drawings. On these drawings:

• The figure 1 is a general diagram of a servo loop of a motion simulator;
• The figure 2 is a general diagram of a corrector according to the prior art of the PID type for an implementation in the control loop of the figure 1 ;
• The figure 3 is a block diagram representing the principle of the so-called standard state control method by means of a corrector incorporating a Kalman filter and a feedback on an estimated state of the mechanical device, used in the method according to the invention;
• The figure 4 is a diagram representing, in the form of an algorithm, the initial step of the method according to the invention for obtaining a robust corrector vis-à-vis the parameters of the system to be controlled;
• The figure 5 schematically shows the servo loop in the test step of the method according to the invention;
• The figure 6 is a graph representing the position corresponding to the setpoint applied at the input of the corrector of the figure 5 during the test step;
• The figure 7 is a diagram representing, in the form of an algorithm, the step of the method according to the invention for determining an optimal corrector adapted to the load.

The method according to the invention allows the automatic adjustment of a servo control loop of a motion simulator adapted to a new load. More particularly, the method according to the invention makes it possible to obtain rapidly, of the order of one minute, the optimal corrector to the new load having the desired performance / robustness compromise. By automatic adjustment, it is necessary to understand a setting that does not require the intervention of a technician, and which can be done, for example, by means of a computer capable of performing the various steps of the method according to the invention by executing the instructions of a program stored in appropriate memory means.

In a schematic manner, the method according to the invention allows the synthesis of correctors adapted to the problem. These correctors are adjustable by means of a number of parameters. During the various steps of the method according to the invention, the values of these parameters are adjusted so as to determine a particular corrector that responds to the compromise sought during this step.

The purpose of the initial step of the method according to the invention is to lead to the determination of a robust corrector for the mechanical system to be enslaved. To do this, it is necessary to use a first physical modeling of the behavior of the mechanical device.

This first modeling is a linear modeling of a system that corresponds to the mechanical part of the mechanical device intervening in the servo loop. The axis of the motion simulator is controlled by a motor of the DC or synchronous type autopilot ("brushless"). This motor is itself controlled by current. By neglecting the electrical dynamics of the motor windings, the torque ┌ (measured in Nm) generated by the motor is proportional to the intensity I (in A) of the applied current: r = Kt · I

$$\frac{\mathit{d\theta }}{\mathit{dt}}=\mathrm{\Omega }$$

The proportionality factor is called the torque constant K _t . The system considered obeys the fundamental law of dynamics: $$\frac{\mathit{d}\mathrm{\Omega }}{\mathit{dt}}\mathit{=}-\frac{\mathit{f}}{\mathit{J}}\mathit{\cdot }\mathrm{\Omega }\mathit{+}\frac{{\mathit{K}}_{\mathit{t}}}{\mathit{J}}\mathit{\cdot }\mathit{I}$$

$$\frac{\mathit{d\theta }}{\mathit{dt}}=\mathrm{\Omega }$$

$$y=C\cdot x$$

Avec $$x=\left(\begin{array}{c}\mathrm{\Omega }\\ \theta \end{array}\right)\mathrm{et}A=\left(\begin{array}{cc}\frac{-f}{J}& 0\\ 1& 0\end{array}\right),B=\left(\begin{array}{c}\frac{\mathit{Kt}}{J}\\ 0\end{array}\right),$$

et C = (0 1)Expression in which J (in kg.m ² / rad) is the moment of inertia of the system (and thus of the load carried by the plate of the simulator of movements); f (expressed in Nm / rad) is a coefficient of viscous friction; Ω (in rad / s) is the speed of rotation of the plate; and, θ (in rad) is the instantaneous position of the plate. It is common to try to express this modeling according to the states in which the system can be enslaved. By posing x the instantaneous state of the system; U ≡ I the control signal applied at the input of the mechanical system to be controlled; and, y ≡ θ the quantity to be controlled, the above equations can be written in the form of a system of equations called state equations: $$\dot{x}=\frac{\mathit{dx}}{\mathit{dt}}=\mathrm{AT}\cdot x+B\cdot U$$

$$\mathrm{there}=\mathrm{VS}\cdot x$$

With $$x=\left(\begin{array}{c}\mathrm{\Omega }\\ \theta \end{array}\right)\mathrm{and}\mathrm{AT}=\left(\begin{array}{cc}\frac{-f}{J}& 0\\ 1& 0\end{array}\right),B=\left(\begin{array}{c}\frac{\mathit{kt}}{J}\\ 0\end{array}\right),$$

and C = (0 1)

The corrector according to the invention is based on a corrector for example type LQG-H2 said LQG. The synthesis of such a corrector is performed for example using the standard state control methodology. This methodology is described, for example, in the book of Mr Philippe de Larminat entitled "standard state control" published in 2000 by HERMES . As an alternative to the standard state control methodology, the robust pole placement methodology could be used, for example. This methodology is described in the book by Philippe de Larminat entitled "Automatic control of linear systems" published by HERMES. The corrector would then have a polynomial form and would be of RST structure which is the most general form of the correctors controlling systems having a control variable and a measured variable. It is also possible to implement the LQG corrector in RST form.

As shown schematically on the figure 3 This methodology uses a feedback loop in which the corrector 12 itself comprises a Kalman filter 10. The Kalman filter 10 takes as input the control signal U and the vector y _f containing the measured position Y and the instruction r. The vector x _f , corresponding to the estimated state of the system by the filter 10, serves as control signal U after having been multiplied by a line vector - Kc, called state return vector (block 11 on the figure 3 ). The Kalman filter 10 makes it possible, as it were, to estimate the state of the system taking into account the system modeling and the input (U) and output (Y) magnitudes actually applied to the mechanical device.

Advantageously, the Kalman filter assembly 10 and state return vector makes it possible to reject disturbances that can modify the behavior of the system.

During the initial step, the servo loop is closed on a numerical simulation of the real system. This numerical simulation is also based on the equations of dynamics mentioned above. Since the system has been simulated by linear equations, the disturbing couples are simulated by introducing a perturbation F applied to the input of the system. Then, the vector x _f , of the estimated state of the system, has a component which is an estimate of the perturbation F.

The matrices Kc and Kf of the Kalman filter 10 are calculated so that the servo loop brings the system to a stable state.

The parameters for adjusting the corrector obtained according to the standard state control methodology are the matrix Kf and the line vector Kc , the synthesis of which is done by minimizing a quadratic criterion.

• Un premier paramètre To est un paramètre essentiel, qui permet de gérer un compromis entre le choix d'une dynamique de rejet des perturbations à haute fréquence et une grande marge de retard ;
• Un deuxième paramètre Tc permet d'arbitrer un compromis entre la marge de module et l'excitation de la commande ;
• Un troisième paramètre Tr permet de régler la dynamique de suivi de la consigne ;
• Un quatrième paramètre Ko est un facteur de forme permettant de renforcer la robustesse de la boucle d'asservissement (au détriment de la dynamique de rejet des perturbations).

Advantageously, the corrector is expressed not by means of the parameters Kf and Kc, said to be low level, but by means of the following four scalar parameters, said of high level:

• A first parameter To is an essential parameter, which makes it possible to manage a compromise between the choice of a high-frequency disturbance rejection dynamics and a large delay margin;
• A second parameter Tc makes it possible to arbitrate a compromise between the module margin and the excitation of the command;
• A third parameter Tr makes it possible to adjust the tracking dynamics of the setpoint;
• A fourth parameter Ko is a form factor making it possible to reinforce the robustness of the servocontrol loop (to the detriment of the disturbance rejection dynamics).

Such a corrector makes it easy to arbitrate the compromises that inevitably occur in any technique for synthesizing a particular corrector. A PID corrector does not offer such a possibility because each of the adjustment actions of one of the constants K _I , K _D or K _P is coupled with the other two.

An initial step of the method according to the invention is carried out in the factory during the manufacture of the motion simulator. This initial step makes it possible to determine the parameters of a corrector which is robust to the variations of moment of inertia of the axis to be controlled. More specifically, the initial step leads to a corrector guaranteeing the stability of the axis for a range of possible moments of inertia between a minimum moment of inertia Jmin corresponding to the moment of inertia of the empty axis and a maximum moment of inertia Jmax corresponding to the moment of inertia of the axis for a maximum load. The ratio of the maximum moments of inertia Jmax and minimum Jmin can, for example, reach a factor of 10. The maximum moments of inertia Jmax and minimum Jmin can be evaluated during the design of the motion simulator, for example using conventionally used CAD tools.

The nominal moment of inertia Jnom retained for the synthesis of a robust corrector by means of the methodology of the standard state control is such that one has: $$\mathit{Jnom}=\sqrt{{\mathit{J}}_{}\min \mathit{\cdot }{\mathit{J}}_{}\max }$$

The viscous friction f that appears in physical modeling can not be easily known by calculation. This is the reason why the zero value is assigned to the value of the viscous coefficient of friction f. It should be emphasized that this case corresponds to the most unfavorable case since dissipative phenomena generally have a stabilizing effect.

$$\frac{\mathrm{d\theta }}{\mathrm{dt}}\mathrm{=}\mathrm{\Omega }$$

The modeling, called nominal, used for the synthesis of the robust corrector is thus reduced to the equations of state: $$\frac{\mathrm{d\Omega }}{\mathrm{dt}}\mathrm{=}\frac{\mathrm{K}}{\mathrm{J}}\mathrm{\cdot }\mathrm{U}$$

$$\frac{\mathrm{d\theta }}{\mathrm{dt}}\mathrm{=}\mathrm{\Omega }$$

This state equation can be enriched by the dynamics of the current loop (containing among others the current amplifier) to perfect the modeling and the performance of the corrector.

In these expressions, K is an overall coefficient of amplification.

K can be known by the calculation knowing that the motor torque constant and the gain of the amplifier are known by design. In the initial step, the aim of the synthesis is to find a robust corrector that guarantees a good level of static margin and dynamic margin level, regardless of the load on the axis. The algorithm 200 of the figure 4 represents the succession of elementary steps leading to the determination of a robust corrector.

At the beginning of the algorithm 200, the value of the parameter To is arbitrarily low. In step 201, the value of the parameter Tc is taken as equal to the value of To divided by a factor of, for example, 10. In step 202, the value of the parameter Tr is taken as equal to that of To. step 203, the unit value is assigned to the parameter Ko. In general, the simulator has an electronic unit comprising storage means and calculation means. The instructions of a program adapted to implement all or part of the method according to the invention are stored in the storage means. The instantaneous values of the variables used are stored in a memory space whose address is predefined, and read from this space when the calculation means execute an instruction performing an operation using this variable.

Then the algorithm 200 continues in the direction indicated by the line 21. Given the value of each of the parameters To, Tc, Tr and Ko, a corrector C is calculated at step 205 by means of the so-called standard status check.

The execution of the program continues with the loop 210. The loop 210 constitutes a first part of the algorithm 200 during which a search is sought for a corrector C ensuring a margin of module MM greater than a threshold value of module margin MMc for all the configurations of the system, that is to say for all the values of the moment of inertia J between Jmin and Jmax. The threshold module margin value MMc has a predefined value, for example equal to 0.5.

The loop 210 proceeds iteratively as follows: in step 211, the value of the moment of inertia J is taken as being worth the minimum value Jmin. In step 212, the module MM margin of the corrector C determined in step 205 is calculated taking into account this value of the moment of inertia J. At the output of step 212, at step 213, the value the MM module margin is compared with the MMc threshold module margin.

If the CM module margin of the corrector C is less than MMc, the program 200 is oriented at A, to the step 220 as will be described below. On the other hand, if for the value of the moment of inertia J, the module margin MM is greater than the threshold module margin MMc, then the value of the moment of inertia is increased by a predefined value Δj, at the step 214. In step 215, the new value of the moment of inertia J is compared with the maximum value Jmax. If J is less than Jmax, the module margin MM of the corrector C is again calculated, taking into account the new value of the moment of inertia J, by performing step 212 again. The loop 210 takes place as long as J is less than upper bound of the range of moment of inertia considered relevant. As soon as J is equal to Jmax, we leave B at loop 210.

If, in step 213, the module margin MM is smaller than the threshold module margin MMc, a new corrector C must be constructed. For this, in step 220, the current value of the parameter Ko is multiplied by one factor greater than unity, for example 1.1. Then, a new corrector C is determined in step 205. The execution of the program returns to loop 210 to check whether this new corrector C satisfies the condition 213 for all values of the moment of inertia J between Jmin and jmax. As soon as such a corrector C has been found, the program 200 passes into a second part of the algorithm 200 (point B).

In a second part of the initial step, a corrector is sought which provides a delay margin MR greater than a delay margin threshold value MRc for all the configurations of the system, that is to say for all the values of the moment. of inertia J between Jmin and Jmax. The value of the threshold delay margin MRc is predefined.

According to this second part of the algorithm 200, in step 230, the current value of the parameter To is multiplied by a constant greater than unity, for example 1.1. Given this new value of the parameter To, steps 201, 202 and 203 are executed again to determine the value of the various parameters that will be used in step 205 to determine a new corrector C; the value Ko retains its previous value, it is not reassigned in this step. In a schematic manner, the algorithm 200 follows the line indicated by the reference numeral 24. At the end of step 205, the algorithm 200 enters a loop 240. The loop 240 is similar to the loop 210 except that it makes it possible to calculate the delay margin MR and to compare it with the value of the threshold delay margin MRc and this for all the values of the moment of inertia J between the minimum value Jmin and the maximum value Jmax. In step 241, the minimum value Jmin is associated with the current value of the moment of inertia J. In step 242, taking into account the corrector C calculated in the preceding step 205, the delay margin MR is calculated. In step 243, this value is compared with the threshold value MRc. If the delay margin MR is less than the threshold value MRc, the The program 200 is oriented at B to step 230. A new value of the parameter To is calculated, the other parameters of the corrector are updated and a new corrector C is determined before the algorithm returns to the loop 240.

If, in step 243, the delay margin MR is actually greater than MRc, the current value of the moment of inertia J is increased by a value Δj predefined in step 244. Then, in step 245, the new value of the moment of inertia J is compared with the maximum value Jmax. If J is different from Jmax, step 242 is executed again to calculate the new value of the delay margin MR. This loop is executed as, in step 245, the moment of inertia J is less than the maximum moment of inertia Jmax. But as soon as J is equal to Jmax, the algorithm 200 ends, the corrector C thus calculated being a robust corrector for the range of moments of inertia.

Incidentally, it is shown that the second part of the algorithm 200 does not significantly modify the MM module margins obtained in the first part of this same algorithm.

Then, in situ, during the use of the motion simulator and each time a new load has been mounted on the plate, the method according to the invention continues with the use of the parameters of the robust corrector. to set an optimal corrector for the new load. This process is decomposable into three successive stages: a test step, an identification step and then a final step leading to the synthesis of an optimal corrector.

During the test step, we are in the configuration of the figure 5 . During this test which is in a closed loop, a movement of the axis enslaved by the robust corrector obtained at the end of the initial step is carried out in order to characterize the unknown load carried by the axis. This test consists in making a movement of the axis along a predefined position reference profile such as that shown schematically on the figure 6 . This position set profile is designed according to the constraints in acceleration, speed and position not to be exceeded in order not to damage the machine. Other setpoint profiles are possible, but it is nevertheless essential that the speed at which the test takes place reaches a sufficiently high level. significant so that the nonlinear phenomena at base speed do not intervene.

So that the control signal is rich and has a spectrum as wide as possible, a pseudo random binary sequence (SBPA), indicated in dotted line on the figure 5 , may alternatively be added to the signal corresponding to the setpoint profile. The amplitude of the pseudo-random bit sequence is calibrated so that this signal does not call into question the direction of rotation of the motion simulator and does not cause a violation of the constraints on the acceleration of the speed and position of the motion simulator. 'axis.

During this test step, the data corresponding to the input variables (values of the command U) and output variables (in this case the measurement of the position Y) are stored as a function of time.

The stored data is pretreated to make them usable for the next identification step. For a given instant t, this pretreatment consists in deriving the measured position signal Y in order to extract a measurement of the instantaneous speed of the axis of the simulator. Then, if the measured speed is less than a speed threshold value, the pretreatment then consists of eliminating the control data U and the measured position Y associated with this instant t. Thus, some nonlinear phenomena occurring at low speed, also called Stribeck effect, are not taken into account.

The method then comprises a step of identifying the system for a specific load. More precisely, this identification step makes it possible to determine the value of the parameters of a second physical modeling of the considered system (inertia, friction, etc.) by exploiting data recorded during the test step.

$$\frac{\mathit{d\theta }}{\mathit{dt}}\mathrm{=}\mathrm{\Omega }$$

The second physical modeling of the system to be enslaved must take into account the nonlinearities affecting the system to be enslaved. Dry friction and / or unbalance can be modeled. Unbalance is the unbalance, along axes that are not vertical, of a mechanical part that is due to the fact that its center of gravity is not on the axis of rotation. Thus, a nonlinear modeling of the axis can be written: $$J\frac{d\mathrm{\Omega }}{\mathit{dt}}=-f\cdot \mathrm{\Omega }+\Gamma -\mathit{fs}\cdot \mathit{sign}\left(\mathrm{\Omega }\right)-d\cdot \sin \left(\theta +\phi \right)$$

$$\frac{\mathit{d\theta }}{\mathit{dt}}\mathrm{=}\mathrm{\Omega }$$

In this system of equations, J is the moment of inertia of the whole system, f a coefficient of viscous friction; Fs the Coulomb modulus of dry friction; a pair of unbalance (d is zero in the case of a vertical axis); φ the angle of the straight line connecting the center of gravity of the load to the axis with respect to the vertical.

In a multiaxis system other forces can intervene in a non-linear way such as, for example, Coriolis forces.

$$\frac{\mathit{d\theta }}{\mathit{dt}}\mathrm{=}\mathrm{\Omega }$$

The term Fs · sign (Ω) modeling dry friction has the property of not being differentiable around zero. In order to avoid the problems relating to this non-differentiability in the identification step, the setpoint during the test step is chosen such that sign (Ω) is constant (for example positive). Under these conditions, the model described previously becomes: $$J\frac{d\mathrm{\Omega }}{\mathit{dt}}=-f\cdot \mathrm{\Omega }+\Gamma -\mathit{fs}-d\cdot \sin \left(\theta +\phi \right)$$

$$\frac{\mathit{d\theta }}{\mathit{dt}}\mathrm{=}\mathrm{\Omega }$$

The parameters J and f of this second model are determined by identification using a non-linear programming algorithm such as the Levenberg-Marquardt algorithm for example.

Finally, the process ends with a step of synthesizing an optimal corrector for the load actually on board. This corrector is the most efficient possible in the sense that it has a response time in low regulation (while maintaining margins of static robustness - margin module- and / or dynamic -marge delay sufficient).

As in the initial step, during the final step, the synthesis of the optimal corrector is performed according to the so-called standard state control methodology by executing the algorithm 300 of the figure 7 . The optimal corrector which satisfies the target delay margin MRc, the target module margin MMc and the adjustment parameter Tr are then determined. this final step uses the moment of inertia obtained by identification during the preceding identification step.

The algorithm 300 begins with the step 301 in which a sufficiently high multiple of the current value of the parameter MRc, for example 30 x MRc, is assigned to the value of the parameter To. The algorithm continues with the step 302, during which the value of To is divided by five and the result is assigned to the parameter Tc. Then, considering the current To, Tr and Tc parameters, step 305 makes it possible to determine the corresponding corrector, by means of the standard state control methodology. It should be noted that step 305 is identical to step 205 of algorithm 200 ( figure 4 ) with Ko set to the unit value. At the output of step 305, step 306 is executed. It makes it possible to calculate the margin of delay MR of the corrector obtained. In step 307, the calculated value of the delay margin MR is compared with the threshold delay margin MRc. If the delay margin MR is indeed greater than MRc, the algorithm 300 returns to step 308 according to the path A. At step 308, a new value of the parameter To is calculated. The new value of To is lower than the previous value, and is obtained by multiplying the previous value of To by a parameter less than unity, in this case 0.95 for example. Then step 302 is executed again. Given the value of the new parameters, a new corrector C is calculated in step 305. The loop is executed as long as condition 307 is verified.

When MR is effectively below the threshold value MRc, the algorithm 300 exits and executes step 310 consisting simply of assigning the previous value to the value of the parameter To used in the last iteration of the loop. Thus, the current value of To is divided by 0.95 for example and the result is assigned as a new value of To.

Then the algorithm 300 at B is conducted at step 311. The second part of the algorithm 300 makes it possible to determine the corrector that will have the best adapted MM module margin. In step 311, the variable Krob, which is equal to the ratio of the parameter To on the parameter Tc, takes the value 5 for example. Then the algorithm 300 continues to step 320 where the values of the parameter To and the parameter Krob are read and the value of Tc is calculated by dividing To by Krob. Then step 305 is executed again, taking into account the current value of the different parameters. A corrector C is determined. In step 321, the margin module MM of this new corrector C is calculated. In step 322, the value of the obtained MM module margin is compared with the threshold module margin MMc. When the module margin MM is less than MMc, the algorithm 300 is directed to step 330 by the link C. At step 330 a new value is calculated for the variable Krob, for example by increasing Krob by one. predetermined value of 0.1 for example. Then steps 320, 305, 321 are executed again, taking into account the new values of the various parameters. Then, the condition 322 is again tested on the value of the module margin MM of the new corrector C. The loop C takes place as long as the module margin MM remains lower than the threshold module margin MMc. As soon as condition 322 is no longer satisfied, algorithm 300 ends. At this moment, the algorithm 300 ends.

An optimal corrector for the load currently placed on the motion simulator plate has been obtained automatically. The method for obtaining such an optimal corrector is reproducible and makes it possible to obtain a result which is reliable and which is the best possible given the values given to the adjustment parameters during the initial step. Tests of implementation of the method according to the invention show that it is possible to define the corrector parameters quickly.

Although the invention has been described with reference to a particular embodiment, it is not limited to this embodiment. It includes all the technical equivalents of the means described as well as their combinations which come within the scope of the invention.

More particularly, the method according to the invention applies to the case of mechanical devices allowing the movement of the plate in rotation along one or more axes, in translation along one or more axes or the combination of rotational and translational movements. In a particular case, the modeling of the mechanical part to be enslaved and the position or positions measured to form the loop enslavement will be chosen according to this case. In particular in the case of a translational movement, the mass of the load will be the inertia parameter to be considered, and no longer the moment of inertia, a parameter of inertia specific to a rotation.

Claims (16)

1. A tuning method to be implemented in a motion simulator able to embark a payload, said simulator including a mechanical device and a control unit, the mechanical device including driving means in order to move a plate capable of carrying the payload ; a current amplifier capable of actuating the driving means in response to a control signal ; a sensor capable of measuring a position of said plate; and said control unit including a corrector capable of transmitting the control signal relative to a position setting signal and to said measured position,
   characterised in that it enables an automatic tuning of said corrector for a position feedback control of the motion of said plate embarking a given payload, said method including:

   - an initial step consisting in the synthesis of a robust corrector, said synthesis being based on a first physical modelling of the mechanical device including one inertia parameter, said obtained robust corrector enabling to feedback control said mechanical device over a range of values of said inertia parameter extending between a minimum inertia parameter and a maximum inertia parameter; and, after having positioned said given payload on the plate;

   - a test step during which the mechanical device, controlled by means of said robust corrector determined during the initial step is actuated according to a predefined position setting profile complying with constraints on the acceleration, the speed and the position of the motion, said control signal and said measured position being stored continuously as data of the test step;

   - an identification step which, on the basis of the data of the test step, enables to determine the value of a plurality of physical parameters of a second modelling of the mechanical device embarking said given payload, said plurality of physical parameters including at least the inertia parameter; and,

   - a final step consisting in the synthesis of an optimal corrector adapted to said given payload, wherein the inertia parameter takes the value of the inertia parameter determined during the identification step.
2. A method according to claim 1, characterised in that said mechanical device is at least able to translate said plate embarking a payload along one axis, the inertia parameter being then a mass of inertia.
3. A method according to claim 1, characterised in that said mechanical device is at least able to rotate said plate embarking a payload around an axis, the inertia parameter being then a moment of inertia.
4. A method according to one of the previous claims, characterised in that during the initial step, the corrector is in a position closed feedback control loop on a digital simulation of the mechanical device embarking a payload having a nominal inertia parameter in said range.
5. A method according to one of the previous claims, characterised in that all the test, identification and final steps are carried out again at least each time the payload is changed.
6. A method according to one of the previous claims, characterised in that, the first modelling is a linear modelling of the dynamic behaviour of the mechanical device.
7. A method according to one of the previous claims, characterised in that said robust and optimal correctors include a Kalman filter based on said first modelling, said Kalman filter taking, as input, the control signal, said measured position and said position setting to generate, as output, an estimated state of said mechanical device, said estimated state being applied as a control signal after having been multiplied by a vector.
8. A method according to claim 7, characterised in that said Kalman filter enables to estimate the disturbances affecting said mechanical device by modelling them by a signal added to the control signal at the input of the mechanical device to be controlled.
9. A method according to one of the previous claims, characterised in that the synthesis of said robust and optimal correctors is preformed by means of a standard state control methodology.
10. A method according to one of the previous claims, characterised in that the robust or optimal correctors include four high-level scalar tuning parameters.
11. A method according to claim 10, characterised in that said initial step comprises first of all, while varying a first scalar parameter among the scalar parameters, looking for a corrector having a modulus margin lower than a threshold modulus margin for all the values of the moment of inertia of said range of moment of inertia, and then, while varying another scalar parameter among the scalar parameters, so-called the second parameter, looking for a corrector having a delay margin lower than a threshold delay margin for all the values of the moment of inertia of said range of moment of inertia.
12. A method according to claim 10 or claim 11, characterised in that, the value of the moment of inertia having been identified, said final step comprises first of all, while varying the second parameter, looking for a corrector having a delay margin greater than said threshold delay margin, and then, while varying still another scalar parameter among said four scalar parameters, so-called the third parameter, looking for an optimal corrector having a modulus margin greater than said threshold modulus margin.
13. A method according to one of the previous claims, characterised in that during the identification step, the second modelling is a linear modelling of the behaviour of the device.
14. A method according to one of the claims 1 to 12, characterised in that, during the identification step, the second modelling takes into account explicitly the forces leading to a non linear behaviour of the device.
15. A method according to one of the previous claims, characterised in that it includes, after completion of said test step, a pre-treatment step in order to reject the data for which the corresponding value of the speed of said plate is lower than a threshold speed.
16. A motion simulator capable of embarking a payload, said motion simulator including a mechanical device and a control unit, the simulator including a mobile plate capable of carrying said payload; driving means capable of putting said plate in motion according to at least one axis; a current amplifier capable of actuating the driving means in response to a control signal; a sensor capable of measuring a position of said plate; the control unit including a corrector capable of transmitting the control signal relative to a position setting signal and said measured position, characterised in that the control unit is configured to implement the tuning method according to any of the claims 1 to 15 to obtain an optimal corrector for a given payload.

Images